# Wind Engineering Module 4.1 Blade Element Theory

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```Wind Engineering
Module 4.1
Blade Element Theory
Lakshmi N Sankar
[email protected]
Recap
• In Module 1, we looked at an overview of the
course objectives, syllabus, and deliverables. We
also reviewed history of wind technology,
nomenclature, and case studies.
• In Module 2, we looked at the wind turbine as an
actuator disk, and established the theoretical
maximum for power that may be captured.
• In module 3, we reviewed airfoil aerodynamics,
and discussed how to compute lift and drag
coefficients. We also reviewed airfoil design
issues.
OVERVIEW
• In this module 4.1, we will review the basics of
blade element theory.
• In module 4.2, we will talk about public
domain solvers, and show how to use these.
• When module 4.2 is done, you are ready to
validate one of these solvers using available
wind turbine data.
– This will be the second deliverable for this course.
Blade Element Theory
• We look at a reference blade from a multi-blade system (typically 2 or 3).
– Blade, geometry, wind speed, blade RPM, and blade pitch angle are assumed
to be known or chosen.
• We divide the blade into strips, aka blade elements.
• On each strip/element
– We find the local section angle of attack.
– We look up the corresponding lift and drag coefficients from a table of airfoil
characteristics.
– We correct these for tip losses, root losses, stall delay, swirl losses as needed.
– We find lift and drag forces.
– We find the propulsive force (in the plane of rotation)
– We find the torque contribution of that strip.
• Sum up the toque contribution over all strips to find torque for one blade.
• Multiply by the number of blades, B.
• Vary the wind speed and compute the entire performance map.
Calculation of Angle of Attack
• The figure on the right is from
AeroDyne Theory manual, found
in the resource section.
– b is pitch angle (known from
from blade geometry)
– U∞ is wind speed
– a is the axial induction factor
(axial induced velocity v divided
by wind speed), discussed later.
– a’ is a tangential induction
factor (tangential induced
velocity divided by wr),
discussed later.
– lr is the local speed ratio Wr/
U∞
Lift and Drag are functions of Angle of
Attack, a
• Once a is known, we can
look up lift and drag
coefficients: Cl and Cd .
• Unfortunately, these
quantities influence the axial
induction factor a and the
tangential induction factor a’.
• An iteration is needed as
discussed later.
• If Cl and Cd are known, we
can find sectional forces and
torques as shown on the
right side.
Thrust generated by the Strip of
width dr and chord c, for all
the blades, B:
Torque generated by the Strip of
width dr and chord c, for all
the blades, B:
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